Question

If the number of diagonals in a polygon is $44$ then find its number of sides.

Answer 1

If $n$ is the number of sides of the polygon, then the number of diagonals of a polygon is $\frac{n\left(n-3\right)}{2}$.

Therefore,

$44=\frac{n\left(n-3\right)}{2}$

$n^2-3n=88$

$n^2-3n-88=0$

$n^2-11n+8n-88=0$

$\left(n-11\right)\left(n+8\right)=0$

$n=11,n=-8$

Since the side cannot be negative, so, the number of sides of the polygon is 11.